Reliability and interval estimation of type-H censored electrical insulation data

The paper presents some analytical results pertaining to the estimation of variance of the parameters of a three parameter Weibull distribution (3pW) under type-II censoring. Ageing failure data acquired on an insulating material of considerable application potential has been used to demonstrate the results. The point estimates of the parameters of failure time distribution are obtained using maximum likelihood estimation method. The true value of the variance of the ML estimates for 3pW are hard to obtain and the situation becomes more complex when the data is censored. The asymptotic variance can be obtained by taking the inverse of the Fisher information matrix, the computation of which is quite involved in the case of censored 3-pW data. Approximations are reported in the literature to simplify the procedure. The authors have considered the effects of such approximations on the precision of variance estimates when the sample size is greatly limited by practical difficulties in obtaining the authentic data. A detailed study of the effect of censoring on the ML estimates, under this condition is also presented.